Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26011959 | C2 | semidirect |
| 3. #26011585 | C2 | semidirect |
| 4. #26011578 | C2 | semidirect |
| 5. #26011573 | C2 | semidirect |
| 6. #26011485 | C2 | semidirect |
| 7. C2×C8×Dic173 | C2 | semidirect |
| 8. #427×C173 | C2 | semidirect |
| 10. #19149701 | C4 | semidirect |
| 30. #14583826 | C2×C4 | semidirect |
| 37. Dic692 | C2×C4 | semidirect |
| 38. #14583815 | C2×C4 | semidirect |
| 39. D1384 | C2×C4 | semidirect |
| 49. C2×C8×C173 | C2×C4 | semidirect |
| 87. Dic173 | #135 | semidirect |
| 92. C173 | C4×#135 | semidirect |
| 99. #427 | D173 | semidirect |
| 136. C2×C8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| #26011959 | 2 |
| #26011585 | 2 |
| #26011578 | 2 |
| #26011573 | 2 |
| #26011485 | 2 |
| C2×C8×Dic173 | 2 |
| #427×C173 | 2 |
| C4×#135 | 173 |